with \(m\)  being the total mass parameter of the quantum constituent, and \(\,h_{\mu \nu }\) 
denoting the (induced) metric of the three-dimensional spatial hypersurfaces of
constant cosmic time. One can, as usual, express \(\,h_{\mu \nu } = g_{\mu \nu } + u_\mu u_\nu \,\) , where \(\, u_\mu = (\hbar /m) \,\partial _\mu S \,\)  is the world velocity of the
evolving (quantum) cosmic `fluid', which can appropriately be taken to be a BEC of
rest mass \(m\)  and described by a macroscopic wave-function of the form (REF ),
provided the value of \(m\)  remains within certain limit
[1]}, [2]}.
